Long ago, shipbuilders
used to frame wooden hulls by sight, but at some point rational principles
took over. There are many ways to generate systematically varying families
of curves on a flat surface. One such family that lends itself to both graphical
and mathematical production is that of the conic sections. Conics were sometimes
used for ship lofting -- "lofting" means drawing full-sized patterns, so called
because it was often done in large, lightly-constructed mezzanines or lofts
above the factory floor -- and adopted for aircraft design in the 20th.
The people who did this kind of layout work, originally using flexible rulers
called splines held in place by weights called ducks, were called "loftsmen."
A North American Aviation mathematician, Roy Liming, was responsible for putting
aircraft lofting on a purely mathematical footing. Supposedly the beautiful
Mustang was the first airplane to be entirely lofted in this way. Liming believed
(incorrectly) that the Mustang's superlative performance was due to the precision
of its surface contours.

Around 1980 I began writing
BASIC software that generated airplane lines using mathematically derived
conics. At first, it generated only cross-sections. The original program,
running, or rather strolling, on a Radio Shack TRS-80, was called BLOFTER,
for "Bulkhead Lofter." I didnít have a printer -- they weren't being given
away yet then -- and to preserve my results I would photograph the screen.

BLOFTER became the three-dimensional
FLOFT ("Fuselage Loft"), written in C, and FLOFT eventually merged with a
separate wing lofting program, WLOFT, to become LOFTSMAN (written in a mixture
of C and C++). All of the lines of Melmoth 2 were generated mathematically
by FLOFT and LOFTSMAN.

The lines of the original
Melmoth were generated graphically. This was easily done because the airplane
was skinned with metal, which does not lend itself to compound curves. The
longitudinal lines were therefore mostly straight, and so it was necessary
to define only a few cross-sections and then to interpolate the ones between
them.

Melmoth 2, on the other
hand, is a composite airplane, and like most composite airplanes it tries
to make the most of the medium by clothing itself, or at least its fuselage,
entirely in compound curves. It's very difficult to define the shape of a
compound-curved surface otherwise than by lofting -- a good definition of
shape is needed for designing the interior structural components -- and so
LOFTSMAN, or some other program like it, is a prerequisite for designing free-form
composite airplanes. Most ordinary CAD programs will not do; they marshal
only a relatively limited vocabulary of curves.

Melmoth 2's fuselage is
lofted in several pieces: a main body, canopy, and a cowling scoop. The program
combines them into a single shape. In addition to the shapes of cross-sections,
canted sections, intersections, and longitudinal components like longerons,
it calculates surface area, volume, and, for purposes of weight estimation,
the centroids of the surface area and volume of the entire fuselage or of
any segment of it. Here is a composite of some of the lines used or generated
by LOFTSMAN, including wing geometry with spar locations (orange) and fuselage
intersection, master longitudinal lines for the fuselage components (black
and violet), vertical cross-sections at intervals of 20 inches (black), and
the line of intersection (blue) between the canopy and the body. Circles with
crosses represent the aerodynamic centroids of the wing, vertical fin, and
horizontal stabilizer.

One of the virtues of
a mathematical loft is that it is necessarily fair. You can change a longitudinal
contour, and the entire fuselage reshapes itself to accommodate the new line
without losing its overall smoothness. And, because you know the exact location
of the surface at any point, it's easy to plan the installation of interior
structure, mechanisms, equipment and furnishings.

When I needed to build
tooling for the wing, the program plotted chordwise wing contours at 10-inch
intervals. These were glued to particle board, cut out, and secured to a tabletop
in order to make a series of cradles for the female molds in which the wing
skins, four of them, were laid up. As would be expected, given the precision
of the loft, the top and bottom skins of each wing fitted together perfectly.
Not only does the program calculate total wing tank volume, but it also does
so for partial fuel loads and for any aircraft attitude. I was therefore quickly
able to determine the amount of usable fuel in various flight attitudes, and
to predict the fuel quantities that would correspond to various positions
of the sender floats, of which there are two in each wing, one in the root
rib and one at mid-span.

LOFTSMAN provides a procedure
for designing flaps to fit in an existing wing, and also for designing the
tracks and actuators required to make the flaps follow a desired path. Since
Melmoth 2 has a large Fowler flap that translates aft all the way to the trailing
edge of the wing before deflecting 30 degrees, the track geometry was relatively
critical. Here is the roller track design screen. To define a roller track,
you first set several points along the flap travel; you then move the roller
around with the mouse, and the slot shape constantly changes to produce the
desired travel.

If you're curious to learn
more about conic lofting, you can download a free demo version of LOFTSMAN
from the AeroLogic website at www.aerologic.com,
together with documentation. I sell the program for $295 in a version that
does lofting only; the version advertised on the website, which also performs
meshing for computational fluid dynamics models, is more expensive.